Question

In 1933, the Consumer Price Index was $38.3(1967=100)$ and Babe Ruth received a salary of $$\mathrm{\$}80,000$$, his highest ever. Near the end of the 1978 baseball season, the Consumer Price Index hit 200 . Using this information, what would Ruth's salary be in $1978?$

Short answer

Babe Ruth's salary in 1978, adjusted for inflation using the given CPI values, would be approximately $417,600.

Step-by-step solution

Understand the concept of CPI

Consumer Price Index (CPI) is a measure that examines the weighted average of prices of a basket of consumer goods and services, such as transportation, food, and medical care. It is calculated by taking price changes for each item in the predetermined basket of goods and averaging them. Changes in the CPI are used to assess price changes associated with the cost of living. In this exercise, we will use the CPI values to adjust Babe Ruth's salary for inflation.

Calculate the CPI ratio

The first step is to calculate the ratio of the CPI in 1978 to the CPI in 1933, which will give us the rate at which we need to adjust Babe Ruth's salary. The formula we can use for this is: CPI ratio = $\frac{CP{I}_{1978}}{CP{I}_{1933}}$ Plug in the given values: CPI ratio = $\frac{200}{38.3}$

Calculate Babe Ruth's adjusted salary

To find Babe Ruth's adjusted salary in 1978, multiply his 1933 salary by the CPI ratio. The formula we can use for this is: Adjusted salary = Salary in 1933 × CPI ratio Plug in the given values: Adjusted salary = $80,000 × $\frac{200}{38.3}$

Solve for the adjusted salary

Now we just need to solve for the adjusted salary: Adjusted salary = $80,000\times \text{(}\frac{200}{38.3}$ ≈ \)80,000 × 5.22 Adjusted salary ≈ $417,600 In conclusion, if Babe Ruth's 1933 salary of $80,000wereadjustedforinflationusingthegivenCPIvalues,hissalaryin1978wouldbeapproximately$417,600.

Key concepts

Inflation Adjustment

Inflation adjustment is an important economic concept that helps us understand how the value of money changes over time. It refers to the process of adjusting prices and salaries to account for inflation, which is the general increase in prices and the decrease in the purchasing power of money.
To adjust for inflation, we often use the Consumer Price Index (CPI). The CPI compares the price level at two different times and helps us calculate how much more expensive goods and services have become.
Understanding inflation adjustment is crucial for financial planning, as it ensures money retains its value over time. As seen in Babe Ruth's salary adjustment, using the CPI ratio allows us to estimate his earning power if we account for the change in the cost of goods from 1933 to 1978.

Cost of Living

The concept of cost of living is closely tied to inflation and the CPI. It represents the amount needed to maintain a certain standard of living in a particular time and place. Factors influencing the cost of living include housing prices, food expenses, taxes, and healthcare costs.

• Higher cost of living means more money is required for the same lifestyle.
• Inflation can increase the cost of living as prices rise.
• Adjustments using CPI help measure changes in living costs over time.

In Babe Ruth's context, understanding the cost of living helps us see why the dollar amount of his salary had to be adjusted for the inflationary effects on goods and services.

Salary Calculation

Salary calculation with regards to inflation is about determining how much a salary from the past is worth today. This requires using the inflation rate, often derived from the CPI, to determine the value. The adjusted salary reflects the equivalent purchasing power in today's terms.
Using the formula: $$\text{Adjusted Salary}=\text{Old Salary}\times \left(\frac{\text{CPI today}}{\text{CPI then}}\right)$$allows us to calculate this figure.
In the exercise, Babe Ruth's salary from 1933 was calculated to give a 1978 equivalent, illustrating how his historical salary compared to the earnings of the time.

Economic History

Economic history provides the context for understanding how past financial conditions influence current decisions and trends. Learning about events like the Great Depression or oil crises gives insight into fluctuations in prices that influence economies.

• Economic events affect inflation rates and consequently consumer behavior.
• Understanding history allows us to grasp long-term growth and economic health.
• Historic salary adjustments help compare financial conditions across different time periods promptly.

For Babe Ruth's salary, placing his earnings in this historical context shows the impact of inflation on economic conditions and personal incomes over several decades.